Journal of the Ramanujan Mathematical Society

Volume 28, Issue 1, March 2013 pp. 19--48.

Automorphic forms, cohomology and CAP representations. The case GL₂ over a definite quaternion algebra

Authors: Harald Grobner
Author institution: Fakultät für Mathematik, Nordbergstraße 15, A-1090 Wien, Austria

Summary: In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group G=GL₂ over a definite quaternion algebra D/Q. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having cohomology in degree 1. The latter ones turn out to be CAP-representations, though G satisfies Strong Multiplicity One.

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